Consider this joint probability distribution P:
P(x1; y1; z1) = 0:03
P(x1; y1; z2) = 0:27
P(x1; y2; z1) = 0:04
P(x1; y2; z2) = 0:16
P(x2; y1; z1) = 0:09
P(x2; y1; z2) = 0:21
P(x2; y2; z1) = 0:08
P(x2; y2; z2) = 0:12
(a) Determine whether P constitutes a Bayesian network with the DAG X -> Y -> Z:
(b) Determine whether P constitutes a Bayesian network with the DAG X -> Z <- Y: